本文摘于《Race Car Vehicle Dynamics》
作者：William F. Miliken and Douglas L. Miliken
Steering systems
Introduction
This chapter begins with a discussion of steering geometry—caster
angle ,trail ,kingpin inclination ,and scrub radius .The next section discuss Ackermann geometry followed by steering racks and gears .Ride steer (bump steer ) and roll steer are closely related to each other ;without compliance they would be the
same .Finally ,wheel alignment is discussed .this chapter is tied to chapter 17 on suspension geometry –when designing a new chassis ,steering and suspension geometry considerations are high priorities . 19.1 steering geometry
The kingpin in a solid front axle is the steering pivot .In modern independent
suspensions , introduced by Maurice olley at Cadillac in 1932,the kingpin is replaced by two (or more ) ball joints that define the steering axis .This axis is not vertical or centered on the tire contact patch for a number of reason .see figure 19.1 to clarify how kingpin location is measured .
In front view ,the angle is called kingpin inclination and the offset of the steering axis from the center of the tire print measured along the ground is called scrub (or scrub radius ). The distance from the kingpin axis to the wheel center plane , measured horizontally at axle height ,is the spindle length .
In side view the kingpin angle is called caster angle ; if the kingpin axis does not pass through the wheel center then side view kingpin offset is present ,as in most motorcycle front ends .The distance measured on the ground from the steering axis to the center of the tire print is the trail (called caster offset in ref .1 )
Kingpin front view geometry
As mentioned in chapter 17, kingpin inclination ,spindle length ,and scrub are usually a compromise between packaging and performance requirements .Some factors to consider include :
1.With a positive spindle length (virtually every car is positive as shown in figure 19.1) the car will be raised up as the wheels are steered away from center .
The more the kingpin inclination is tilted from vertical the more the car will be raised when the front wheels are steered .This effect always raises the car , regardless of which direction the wheel is steered ,unless the kingpin inclination is true
vertical .the effect is symmetric side to side only if there is no caster angle .See the following section on caster angle .
For a given kingpin inclination ,a longer positive spindle length will increase the amount of lift with steer .
2.The effect of kingpin inclination and spindle length in raising the front end ,by itself ,is to aid centering of the steering at low speed .At high speed any trail will probably swamp out the effect that raise ad fall have on centering .
3. Kingpin inclination affects the steer –camber characteristic .when a wheel is steered ,it will lean out at the top ,toward positive camber ,if the kingpin is inclined in the normal direction (toward the center of the car at the upper end ). Positive camber results for both left– and right-hand steer .the amount of this effect is small ,but significant if the track includes tight turns.
4. When a wheel is rolling over a bumpy road ,the rolling radius is constantly changing ,resulting in changes of wheel rotation speed . This gives rise to longitudinal forces at the wheel center .The reaction of these forces will introduce kickback into the steering in proportion to the spindle length .If the spindle length is zero then there will be no kick from this source .Design changes made in the last model of the GM ―P ‖car (fiero ) shortened the spindle length and this resulted in less wheel kickback on rough roads when compared to early model ―P ‖cars.
5. The scrub radius shown in figure 19.1 is negative ,as used on front-wheel –drive cars (see below ) . driving or braking forces (at the ground ) introduce steer torques proportional to the scrub radius . If the driving or braking force is different on left and right wheels then there will be a net steering torque felt by the driver
(assuming that the steering gear has good enough rev erse efficiency ).The only time that this is not true is with zero scrub (centerpoint steering ) because there is no moment arm for the drive (or brake ) force to generate torque about the kingpin .
With very wide tires the tire forces often are not centered in the wheel center plane due to slight changes in camber ,road surface irregularities ,tire nonuniformity (conicity ),or other asymmetric effects .These asymmetries can cause steering kickback regardless of the front view geometry .Packaging requirements often conflict with centerpoint steering and many race cars operate more or less okay on smooth tracks with large amounts of scrub .
6. For front drive ,a negative scrub radius has two strong stabilizing
effects :first ,fixed steering wheel –if one drive wheel loses traction ,the opposing
wheel will toe –out an amount determined by the steer compliance in the system .This will tend to steer the car in a straight line ,even though the tractive force is not equal side-to –side and the unequal tractive force is applying a yaw moment to the vehicle .
Second ,with good reverse efficiency the driver’s hands never truly fix the
steering wheel . In this case the steering wheel may be turned by the effect of uneven longitudinal tractive forces ,increasing the stabilizing effect of the negative scrub radius .
Under braking the same is true .Negative scrub radius tends to keep the car traveling straight even when the braking force is not equal on the left and right side front tiresome (due to differences in the roadway or the brakes).
Caster angle and trail
With mechanical trail ,shown in figure 19.1,the tire print follows behind the steering axis in side view .Perhaps the simplest example is on an office chair caster –with any distance of travel ,the wheel aligns itself behind the point .More trail means that the tire side force has a large moment arm to act on the kingpin axis .This produces more self-centering effect and is the primary source of self-centering
moment about the kingpin axis at speed .Some considerations for choosing the caster angle and trail are :
1.More trail will give higher steering force .with all cars ,less trail will lower the steering force .In some cases ,manual steering can be used on heavy sedans (instead of power steering ) if the trail is reduced to almost zero .
2.Caster angle ,like kingpin inclination ,cause the wheel to rise and fall with steer .unlike kingpin inclination ,the effect is opposite from side to side .With
symmetric geometry (including equal positive caster on left and right wheels ) ,the effect of left steer is to roll the car to the right ,causing a diagonal weight shift .In this case ,more load will be carried on the LF –RR diagonal ,an oversteer effect in a left-hand turn .
The diagonal weight shift will be larger if stiffer springing is used because this is a geometric effect .The distance each wheel rises (or falls ) is constant but the weight jacking and chassis roll angle are functions of the front and rear roll stiffness. This diagonal load change can be measured with the car on scales and alignment ( weaver ) plates .
Keep in mind that the front wheels are not steered very much in actual racing , except on the very tightest hairpin turns . For example , on a 100-ft .radius (a 40-50 mph turn ), a 10-ft. wheelbase neutral steer car needs only about 0.1rad .(5.7)of steer at the front wheels (with a 16:1steering ratio this is about 90degree at the steering wheel ).
For cars that turn in one direction only , caster stagger (differences in left and right caster ) is used to cause the car to pull to one side due to the car seeking the lowest ride height . caster stagger will also affect the diagonal weight jacking effect mentioned above .
If the caster is opposite (positive on one side and negative the same number of degrees on the other side ) then the front of the car will only rise and fall with steer ,
no diagonal weight jacking will occur .
3. Caster angle affects steer-camber but ,unlike kingpin inclination ,the effect is favorable . With positive caster angle the outside wheel will camber in a negative direction (top of the wheel toward the center of the car ) while the inside wheel cambers in a positive direction , again learning into the turn .
In skid recovery , ―opposite lock ‖ (steer out of the turn ) is used and in this case the steer–camber resulting from caster angle is in the ―wrong ‖ direction for increased front tire grip . conveniently ,this condition results from very low lateral force at the rear so large amounts of front grip are not needed .
4. As discussed in chapter 2, tires have pneumatic trail which effectively adds to (and at high slip Angles subtracts from ) the mechanical trail . This tire effect is nonlinear with lateral force and affects steering torque and driver feel .In particular , the fact that pneumatic trail approaches zero as the tire reaches the limit will result in lowering the self-centering torque and can be s signal to the driver that the tire is near breakaway .
The pneumatic trail ―breakaway signal‖ will be swamped out by mechanical trail if the mechanical trail is large compared to the pneumatic trail .
5.Sometimes the trail is measured in a direction perpendicular to the steering axis (rather than horizontal as shown in figure 19.1) because this more accurately
describes the lever (moment ) arm that connects the tire lateral forces to the kingpin .
Tie rod location
Note that in figure 19.1 a shaded area is shown for the steering tie rod location . Camber compliance under lateral force is unavoidable and if the tie rod is located as noted ,the effect on the steering will be in the understeer ( steer out of the turn ) direction becomes much more complex than can be covered here . 19.2 Ackerman steering geometry
As the front wheels of a vehicle are steered away from the straight-ahead
position ,the design of the steering linkage will determine if the wheels stay parallel or if one wheel steers more than the other .This difference in steer Angles on the left and right wheels should not be confused with toe-in or toe-out which are adjustments and add to ( or subtract from ) Ackerman geometric effects .
For low lateral acceleration usage (street cars) it is common to use Ackerman geometry . as seen on the left of figure 19.2, this geometry ensures that all the wheels roll freely with no slip Angles because the wheels are steered to track a common turn center . Note that at low speed all wheels are on a significantly different radius , the inside front wheel must steer more than the outer front wheel . A reasonable approximation to this geometry may be as shown in figure 19.3.
According to ref .99, Rudolf Ackerman patented the double pivot steering system in 1817 and in 1878, Charles Jeantaud added the concept mentioned above to eliminate wheel scrubbing when cornering . Another reason for Ackermann
geometry ,mentioned by Maurice olley , was to keep carriage wheels from upsetting smooth gravel driveways .
High lateral accelerations change the picture considerably . Now the tires all
operate at significant slip Angles and the loads on the inside track are less than on the outside track . Looking back to the tire performance curves ,it is seen that less slip angle is required at lighter loads to reach the peak of the cornering force to a higher slip angle than required for maximum side force . Dragging the inside tire along at high slip Angles ( above for peak lateral force ) raise the tire temperature and slows the car down due to slip angle ( induced ) drag .For racing , it is common to use parallel steering or even reverse Ackermann as shown on the center and right side of figure 19.2.
It is possible to calculate the correct amount of reverse Ackermann if the tire properties and loads are known . In most cases the resulting geometry is found to be too extreme because the car must also be driven (or pushed ) at low speeds , for example in the pits .
Another point to remember is that most turns in racing have a fairly large radius and the Ackermann effect is very small . In fact , unless the steering system and
suspension are very stiff ,compliance (deflection ) under cornering loads may steer the wheels more than any Ackermann (or reverse Ackermann ) built into the geometry .
The simplest construction that generates Ackermannn geometry is shown in figure 19.3 for ―rear steer ‖ . Here ,the rack (cross link or relay rod in steering box systems ) is located behind the front axle and lines staring at the kingpin axis ,
extended through the outer tie rod ends , intersect in the center of the rear axle . The angularity of the steering knuckle will cause the inner wheel to steer more than the outer (toe-out on turning ) and a good approximation of ―perfect Ackermann ‖ will be achieved .